Cryptography has expanded into many areas, including post-quantum cryptography (designed to withstand attacks from quantum computers), secure multi-party computation (allowing parties to compute a function without revealing their private inputs), and zero-knowledge proofs (allowing a prover to convince a verifier that a statement is true without revealing the underlying proof).
Theoretical computer science (TCS) is a broad discipline that studies fundamental questions underlying computer-based technologies. For example, it asks how efficiently problems can be solved under limited resources such as time, memory, and power.
There are many fields within or closely related to TCS, including (but not limited to) algorithms, combinatorics, complexity theory, theoretical cryptography (as mentioned above), distributed computing, game theory, graph theory, privacy, and quantum computing.
The following texts provide more information about the topics I am interested.
Algorithms are one of the most foundational topics for any CS student. The goal is to design efficient and optimal algorithms (or approximation algorithms) for problems inspired by machine learning, statistics, high-dimensional geometry, combinatorics, and related areas.
Combinatorics is the study of discrete structures and how they can be counted, arranged, and analysed. It is about finite objects such as graphs, sets, permutations, and networks. Some focuses of this area include graph theory, extremal combinatorics, probablistic combinatorics, enumeration, etc.
Complexity theory studies the limits of efficient computation. In particular, it examines how constraints such as time and memory make certain problems difficult to solve. It asks what kinds of problems are hard and why they are hard. A famous open problem in the field is P vs. NP.
This topic interacts broadly with other areas of theoretical computer science and mathematics, and it uses a range of tools, including Boolean and algebraic circuits, Turing machines, and interactive protocols.
Previously, I have also conducted research in mathematical modelling as part of the field of biophysics. This area specifically applies principles and methods from mathematics and physics to study biological systems such as cells and molecules.